05/14/2009, 11:48 PM
this idea might have been posted before, forgive me if such is the case.
we know exp(x)-1 has a fixed point.
which leads to unique half-iterate and a somewhat unique superfunction.
so we might want to use the fixpoint of exp(x) - 1 for a ' surrogate fixpoint ' of exp(x).
here is how - if i dont blunder - :
using superfunction F(x) :
F(x + 1) = exp [ F(x) ] - 1.
which can be solved by taylor series i believe ?
now the simple but brilliant idea - if correct -
F( x + 1 ) + 1 = exp [ F(x) ]
generalize to
F ( x + a ) + a = exp exp exp ... a times [ F(x) ]
and Coo tetration follows !!?
regards
tommy1729
we know exp(x)-1 has a fixed point.
which leads to unique half-iterate and a somewhat unique superfunction.
so we might want to use the fixpoint of exp(x) - 1 for a ' surrogate fixpoint ' of exp(x).
here is how - if i dont blunder - :
using superfunction F(x) :
F(x + 1) = exp [ F(x) ] - 1.
which can be solved by taylor series i believe ?
now the simple but brilliant idea - if correct -
F( x + 1 ) + 1 = exp [ F(x) ]
generalize to
F ( x + a ) + a = exp exp exp ... a times [ F(x) ]
and Coo tetration follows !!?
regards
tommy1729